Music And Mathematics
Music theorists sometimes use mathematics to understand music. Mathematics is "the basis of sound" and sound itself "in its musical aspects... exhibits a remarkable array of number properties", simply because nature itself "is amazingly mathematical". Though ancient Chinese, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, the Pythagoreans of ancient Greece are the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, particularly the ratios of small integers. Their central doctrine was that "all nature consists of harmony arising out of numbers".
From the time of Plato, harmony was considered a fundamental branch of physics, now known as musical acoustics. Early Indian and Chinese theorists show similar approaches: all sought to show that the mathematical laws of harmonics and rhythms were fundamental not only to our understanding of the world but to human well-being. Confucius, like Pythagoras, regarded the small numbers 1,2,3,4 as the source of all perfection.
To this day mathematics has more to do with acoustics than with composition, and the use of mathematics in composition is historically limited to the simplest operations of counting and measuring. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. Some composers have incorporated the golden ratio and Fibonacci numbers into their work.
Read more about Music And Mathematics: Time, Rhythm and Meter, Musical Form, Frequency and Harmony, Tuning Systems, Connections To Set Theory, Connections To Abstract Algebra, The Golden Ratio and Fibonacci Numbers
Famous quotes containing the words music and/or mathematics:
“If music in general is an imitation of history, opera in particular is an imitation of human willfulness; it is rooted in the fact that we not only have feelings but insist upon having them at whatever cost to ourselves.... The quality common to all the great operatic roles, e.g., Don Giovanni, Norma, Lucia, Tristan, Isolde, Brünnhilde, is that each of them is a passionate and willful state of being. In real life they would all be bores, even Don Giovanni.”
—W.H. (Wystan Hugh)
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)